Papers by Nasser-eddine Tatar
Applicable Analysis, 2015
Communications in Applied Analysis
In this paper we shall investigate the behavior of solutions of an ordinary fractional differenti... more In this paper we shall investigate the behavior of solutions of an ordinary fractional differential problem. Namely, we consider a weighted Cauchy-type problem involving a fractional derivative in the sense of Riemann-Liouville and a non-local term in the second member of the equation. We show that, for certain nonlinearities, solutions decay polynomially on their interval of existence.
Dynamic Systems and Applications
We consider a beam problem with a polynomial source and boundary damping of order between 0 and 1... more We consider a beam problem with a polynomial source and boundary damping of order between 0 and 1. Sufficient conditions on initial data are established to have blow-up of solutions in finite time.
Electronic Journal of Qualitative Theory of Differential Equations, 1999
We consider a basic fractional differential inequality with a fractional derivative named after H... more We consider a basic fractional differential inequality with a fractional derivative named after Hilfer and a polynomial source. A non-existence of global solutions result is proved in an appropriate space and the critical exponent is shown to be optimal.
Nonlinear Analysis: Theory, Methods & Applications, 2008
... Permissions & Reprints. Exponential and polynomial decay for a quasilinear viscoelastic e... more ... Permissions & Reprints. Exponential and polynomial decay for a quasilinear viscoelastic equation. Salim A. Messaoudi Corresponding Author Contact Information , a , E-mail The Corresponding Author and Nasser-eddine Tatar a , E-mail The Corresponding Author. ...
Siberian Mathematical Journal, 2007
ABSTRACT
Boundary Value Problems, 2015
A diffusion problem involving time derivative acting on two time scales represented by two fracti... more A diffusion problem involving time derivative acting on two time scales represented by two fractional derivatives is investigated. The orders of the fractional derivatives are both between 0 and 1 and therefore the problem corresponds to the subdiffusion case. It is considered on a semi-infinite axis and the forcing term and the initial data are assumed compactly supported. To reduce the problem to that support there is a risk of being lead to an "infected" problem due to the reflected waves on the new settled boundary. To avoid this undesirable effect of reflected waves on standard boundaries, we establish artificial boundaries and find the appropriate artificial boundary conditions. Then, using properties of fractional derivatives, a generalized version of the Mittag-Leffler function and some adequate manipulations of inverse Laplace transforms we find the explicit solution of the reduced problem.
Advances in Applied Mathematics and Approximation Theory, 2013
Zeitschrift für Analysis und ihre Anwendungen, 2000
We consider a nonlinear wave equation with an internal damping represented by a fractional time, ... more We consider a nonlinear wave equation with an internal damping represented by a fractional time, derivative and with a polynomial source. It is proved that the solution is unbounded and grows up exponentially in the L-p-norm for sufficiently large initial data. To this end we use some techniques based on Fourier transforms and some inequalities such as the Hardy-Littlewood inequality.
Zeitschrift für Analysis und ihre Anwendungen, 2002
ABSTRACT
Siberian Mathematical Journal, 2007
We consider the Laplace equation in R d−1 × R + × (0, +∞) with a dynamic nonlinear boundary condi... more We consider the Laplace equation in R d−1 × R + × (0, +∞) with a dynamic nonlinear boundary condition of order between 1 and 2. Namely, the boundary condition is a fractional differential inequality involving derivatives of non-integer order as well as a nonlinear source. Nonexistence results and necessary conditions for local and global existence are established. In particular, we show that the critical exponent depends only on the fractional derivative of lowest order.
Opuscula Mathematica, 2013
In this paper the nonlinear viscoelastic wave equation
Nonlinear Analysis: Theory, Methods & Applications, 2005
In this work, we are concerned with a family of nonlinear ordinary differential equations of frac... more In this work, we are concerned with a family of nonlinear ordinary differential equations of fractional order. It is proved that solutions of these equations with weighted initial data exist globally and decay as a power function.
Nonlinear Analysis: Theory, Methods & Applications, 2011
ABSTRACT A nonlinear beam equation describing the transversal vibrations of a beam with boundary ... more ABSTRACT A nonlinear beam equation describing the transversal vibrations of a beam with boundary feedback is considered. The boundary feedback involves a fractional derivative. We discuss the asymptotic behavior of solutions. In fact, we prove that solutions blow up in finite time under certain assumptions on the nonlinearity.
Nonlinear Analysis, 2004
We prove global existence and exponential decay of solutions for a system which arise in thermal ... more We prove global existence and exponential decay of solutions for a system which arise in thermal convection flow. For sufficiently small initial data, these results improve previous ones in (Funkcial. Ekvac. 34 (1991) 449). Further, we investigate the behavior of solutions for arbitrarily large initial data. In particular, we show that the length of the interval on which we have existence and exponential decay is inverse proportional to the size of the initial data.
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Papers by Nasser-eddine Tatar